Given,

$\frac{5}{6}\times \frac{2}{9}÷\frac{4}{9}÷\frac{6}{7}=?$

It can aslo be approximated as

$$\begin{gathered} = \frac{5}{3}\times \frac{1}{9}\times \frac{9}{4}\times \frac{7}{6} \\ =\frac{{\displaystyle 5}}{{\displaystyle 3}}\times \frac{{\displaystyle 1}}{{\displaystyle 4}}\times \frac{{\displaystyle 7}}{{\displaystyle 6}} \\ =\frac{35}{72}= 0.48 \end{gathered}$$

= 0.48 ≈ 0.49

Hence, Option C is correct.